The funny-shaped surface in the Wolfram “CDF” below (software download link) depicts excess demand for goods. The flat one represents the zero line where supply and demand are equal. On each axis is a variable that affects the degree to which demand outpaces or falls short of supply: (1) firms’ share in the price of goods, after paying wages, which equals the pricing markup m divided by (1 + m); and  (2) the income and production generated by the private sector, measured by capacity utilization. The height dimension measures excess demand for goods.

The sliding levers at the top of the CDF allow one to change (1) (“chi”) the percentage of disposable income spent by the wealthy households who own most stock, as well as all government-issued securities; (2) the rate of production by the public sector, which hires workers to produce services; and/or (3) the annual compound real interest rate (yield) on government securities. All of the other parameters are held constant as you move the levers. Click on the “plus” sign next to a lever, and further information appears.

[WolframCDF source=”http://multiplier-effect.org/files/2014/04/3D-excess-demand-graphN5.cdf” width=”331″ height=”361″ altimage=”3D-excess-demand-graphN5.png” altimagewidth=”309″ altimageheight=”351″]

Click here for a much larger, easier-to-read version of this CDF on a webpage of its own.

At the curved line where the two surfaces intersect (the edge of the dark blue region when viewed from above), aggregate demand is just equal to private-sector output, and there is no tendency for capacity utilization to change. Finding this intersection gives us the set of combinations of output and the distributional parameter at which all newly produced units are being sold, and no new goods orders are stacking up unfilled. Experimenting with the CDF, one finds that capacity utilization is usually higher: (1) when the share of the “K-sector”, or capital-owning sector, (m/(1 + m)) is lower, (2) when that sector spends a greater percentage of its disposable income, or (3) when government production and payrolls are larger.

One should keep in mind the simplification required to construct such a “small” model, which in graphical form represents only an imaginary economy; the numbers are not intended to mirror those of any particular country or data set–but the economic  system portrayed in the CDF is meant to be similar in many of its essentials to that of large industrialized nations with their own currencies, huge companies, liquid securities markets, floating exchange rates, etc. Another possible way to interpret this highly “stratified” industrial system is as an entire global economy in a mere 3 sectors: workers; firms/wealthy households; and government/central bank.

A larger version of the model featured an unemployment benefits system. To come: a discussion of the movements over time that may or may not bring the economy closer to the line where excess demand just reaches the flat surface and no higher. The model still has only a rudimentary financial system, with no private borrowing. Hence, the interest rate lever acts upon the economy solely by changing the amount of interest payments from the government to households–a distributional and fiscal variable in its own right and an MMT insight. (Business investment depends on capacity utilization and the gross after-tax profit rate.) The model is drawn more or less directly from Levy Institute working paper 723 (see this previous post) as revised recently for the academic journal Metroeconomica.